Matroid Theory and Chern-Simons

Details Matroid Theory and Chern-Simons Matroid Theory and Chern-Simons

2000-05-12

arxiv.org/abs/hep-th/0005117v1

J.Math.Phys. 41 (2000) 7997-8005

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, Latex

Scientific paper

It is shown that matroid theory may provide a natural mathematical framework for a duality symmetries not only for quantum Yang-Mills physics, but also for M-theory. Our discussion is focused in an action consisting purely of the Chern-Simons term, but in principle the main ideas can be applied beyond such an action. In our treatment the theorem due to Thistlethwaite, which gives a relationship between the Tutte polynomial for graphs and Jones polynomial for alternating knots and links, plays a central role. Before addressing this question we briefly mention some important aspects of matroid theory and we point out a connection between the Fano matroid and D=11 supergravity. Our approach also seems to be related to loop solutions of quantum gravity based in Ashtekar formalism.

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